Peel and dice the potatoes into roughly 1-inch cubes, keeping them uniform for even cooking.
Chop the onion finely and mince the garlic, smashing the cloves first to release a fragrant aroma.
Heat the olive oil in a large pot over medium heat until shimmering, then add the chopped onions. Sauté for about 5 minutes until they turn translucent and smell sweet.
Add the minced garlic to the onions and cook for another minute, releasing a fragrant, nutty aroma as it becomes golden at the edges.
Stir in the diced potatoes, coating them in the fragrant oil and aromatics, then cook for 2 minutes to start softening the potatoes.
Pour in the vegetable broth, enough to cover the potatoes, and bring the mixture to a gentle simmer. Let cook for about 15-20 minutes until the potatoes are tender and easily pierced with a fork.
Once the potatoes are soft, carefully blend the soup directly in the pot using an immersion blender or transfer in batches to a blender, blending until silky and smooth.
Return the pureed soup to a gentle simmer, season with salt, pepper, and optional smoked paprika, then cook for another 5 minutes to meld flavors.
If using greens, stir them in now and cook just until wilted, about 1-2 minutes, for a fresh contrast.
Taste and adjust seasoning as needed, then ladle into bowls and garnish with a drizzle of olive oil or a sprinkle of herbs if desired.
